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# ==============================================================================
# TEMPLATE JAWABAN KUIS
# Komputasi Statistika, Kelas D
# Prodi S1 Statistika FSAD ITS - Semester Genap 2025/2026
# Kamis, 12 Maret 2026
# ==============================================================================
# Nama  : BEATRISIA KAYLLA SIMANJUNTAK
# NRP   : 5003251189
# Kelas : D
# ==============================================================================


# ==============================================================================
# Soal 1 [TOTAL 50 poin] - Winsorized Mean
# ==============================================================================

# Data
data <- c(12, 45, 52, 58, 61, 63, 67, 70, 72, 75, 78, 82, 88, 95, 310)
# --- [a] Buatlah fungsi winsorized_mean(x, alpha) ---
sort_function <- function(data){
  sorted_data <- sort(data)
  return(sorted_data)
}

mean_function <- function(data){
  mean_value <- mean(data)
  return(mean_value)
}

data <- sort_function(data)

winsor_function <- function(data, alpha){
  
  data_sort <- sort_function(data)
  
  n <- length(data_sort)
  k <- floor(n * alpha)
  
  winsor_data <- data_sort
  
  for(i in 1:k){
    winsor_data[i] <- data_sort[k+1]
  }
  
  for(i in (n-k+1):n){
    winsor_data[i] <- data_sort[n-k]
  }
  
  return(winsor_data)
}

winsor_mean <- function(data, alpha){
  
  data_winsor <- winsor_function(data, alpha)
  mean_w <- mean_function(data_winsor)
  
  return(list(
    winsor_data = data_winsor,
    winsor_mean = mean_w
  ))
}


# --- [b] Hitung ordinary mean (alpha=0) dan Winsorized mean 20% (alpha=0.2) ---

# Ordinary mean
# TULIS KODE ANDA DI SINI
result_00 <- winsor_mean(data, 0)
cat("Winsorized data alpha 0 :", result_00$winsor_data, "\n")
cat("Winsorized mean alpha 0 :", result_00$winsor_mean)

# Winsorized mean 20%
# TULIS KODE ANDA DI SINI
result_02 <- winsor_mean(data, 0.2)
cat("Winsorized data alpha 0.2 :", result_02$winsor_data, "\n")
cat("Winsorized mean alpha 0.2 :", result_02$winsor_mean, "\n\n")

# ==============================================================================
# Soal 2 [TOTAL 60 poin] - Weighted Multivariate Descriptive Statistics
# ==============================================================================

# --- Baca data CSV ---
df <- read.csv("C:/Users/HP/Downloads/Quiz 1 Komstat/data_quiz1.csv")
X <- as.matrix(df[, c("x1", "x2", "x3")])
w <- df$w

# --- [a] Buatlah fungsi weighted_corr(X, w) ---

weighted_corr <- function(X, w) {
  # TULIS KODE ANDA DI SINI
  X <- as.matrix(X)
  n <- nrow(X)
  W <- diag(w)
  
  one_n <- matrix(1, nrow = n, ncol = 1)
  nw <- as.numeric(t(one_n) %*% w)
  
  x_bar_w <- (1/nw) * t(X) %*% W %*% one_n
  
  D <- X - (one_n %*% t(x_bar_w))
  
  Sw <- (1/nw) * t(D) %*% W %*% D
  
  sw <- sqrt(diag(Sw))
  
  V_inv <- diag(1/sw)
  Rw <- V_inv %*% Sw %*% V_inv
  
  return(list(
    W = W,
    mean_w = x_bar_w,
    S_w = Sw,
    s_w = sw,
    R_w = Rw
  ))
}

hasil <- weighted_corr(X, w)
print(hasil$W)
print(hasil$mean_w)
print(hasil$S_w)
print(hasil$s_w)
print(hasil$R_w)





# --- [b] Aplikasikan fungsi pada data ---

# Panggil fungsi
# TULIS KODE ANDA DI SINI
hasil <- weighted_corr(X, w)

# Tampilkan vektor mean tertimbang
# TULIS KODE ANDA DI SINI
print(hasil$mean_w)

# Tampilkan matriks varians-kovarians tertimbang
# TULIS KODE ANDA DI SINI
print(hasil$S_w)

# Tampilkan vektor standar deviasi tertimbang
# TULIS KODE ANDA DI SINI
print(hasil$s_w)

# Tampilkan matriks korelasi tertimbang
# TULIS KODE ANDA DI SINI
print(hasil$R_w)

install.packages("ggplot2")
install.packages("corrplot")
library("ggplot2")

# 1. LOAD LIBRARIES (Penting agar tidak error "function not found")
library(ggplot2)
library(corrplot)

# ==============================================================================
# SOAL 1: WINSORIZED MEAN
# ==============================================================================

# Data Awal (Definisikan objek ini dulu!)
data_awal <- c(12, 45, 52, 58, 61, 63, 67, 70, 72, 75, 78, 82, 88, 95, 310)

# Fungsi Winsor (Sesuai kode Anda yang sudah diperbaiki)
winsor_function <- function(data, alpha){
  data_sort <- sort(data)
  n <- length(data_sort)
  k <- floor(n * alpha)
  winsor_data <- data_sort
  if(k > 0){
    for(i in 1:k) winsor_data[i] <- data_sort[k+1]
    for(i in (n-k+1):n) winsor_data[i] <- data_sort[n-k]
  }
  return(winsor_data)
}

# Hitung Winsor 20%
data_winsor_20 <- winsor_function(data_awal, 0.2)
mean_winsor <- mean(data_winsor_20)

# VISUALISASI SOAL 1
library(ggplot2)

df_box <- data.frame(
  Nilai = c(data_awal, data_winsor_20),
  Tipe = rep(c("Original", "Winsorized 20%"), each = length(data_awal))
)

ggplot(df_box, aes(x = Tipe, y = Nilai, fill = Tipe)) +
  geom_boxplot() +
  scale_fill_manual(values = c("steelblue", "skyblue")) +
  labs(title = "Boxplot Perbandingan Data Asli vs Winsorized") +
  theme_minimal()

# ==============================================================================
# SOAL 2: MULTIVARIATE CORRELATION
# ==============================================================================

# Menggunakan matriks korelasi yang Anda dapatkan sebelumnya
# Kita buat matriksnya secara manual agar kode ini bisa jalan (reproducible)
Rw_matrix <- matrix(c(1.0000000, -0.9531095, -0.9558207,
                      -0.9531095,  1.0000000,  0.9891979,
                      -0.9558207,  0.9891979,  1.0000000), 
                    nrow = 3, byrow = TRUE)
colnames(Rw_matrix) <- rownames(Rw_matrix) <- c("x1", "x2", "x3")

# VISUALISASI SOAL 2
corrplot(Rw_matrix, method = "color", addCoef.col = "black", 
         tl.col = "black", title = "\nHeatmap Korelasi Tertimbang", mar=c(0,0,1,0))